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Chapter 11: Q. 14 (page 871)

Completethefollowingdefinition:Ifr(t)=x(t),y(t),z(t)isatwice-differentiablepositionfunction,thentheaccelerationvectora(t)is....

Short Answer

Expert verified

Ifr(t)=x(t),y(t),z(t)isatwicedifferentiablepositionfunction.Then,a(t)=x''(t),y''(t),z''(t)

Step by step solution

01

Step 1. Given information is:

r(t)=x(t),y(t),z(t)beatwicedifferentiablepositionfunction.

02

Step 2. Acceleration Vector

Letcbethecurvedefinedbyr(t)=x(t),y(t),z(t),whichisatwicedifferentiablepositionfunctionontheintervalI⊂R.Thentheaccelerationvectorisgivenby:a(t)=r''(t)a(t)=v'(t)=x''(t),y''(t),z''(t)Thus,a(t)=x''(t),y''(t),z''(t)

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